Array Operations – Exponentiation (^)

For Array Exponentiation.

B=A^2
B=A*A
C=A^3
C=A*A*A

For array multiplication, to be valid i.e.

A*A

the following condition must be met 

<span style="color: #ffcc00;">n1</span>=<span style="color: #00ccff;">m2</span>

. Now for array exponentiation, the two arrays being multiplied are the same thus 

<span style="color: #ffcc00;">n1</span>=<span style="color: #00ccff;">m1</span>

and

<span style="color: #ffcc00;">n2</span>=<span style="color: #00ccff;">m2</span>

 and because 

<span style="color: #ffcc00;">n1</span>=<span style="color: #00ccff;">m2</span>

 the only condition which satisfies the rule of matrix multiplication is that of a square matrix i.e.

<span style="color: #ffcc00;"><span style="color: #00ccff;">m1</span></span>=<span style="color: #00ccff;">m2</span>

.

A=[1,2;3,4]
B=[1,2;3,4]^2
B=[1,2;3,4]*[1,2;3,4]
C=[1,2;3,4]^3
C=[1,2;3,4]*[1,2;3,4]*[1,2;3,4]

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